My card opens the wrong person's profile

That card is still linked to the other person's account. A card opens whoever it is currently claimed by, so this is what a second-hand or passed-on card does until it is released.

If somebody gave you their old card, they need to release it first. They can do that from My Cards in their dashboard by deactivating it. What happens next depends on where the card came from:

A card they bought stays theirs even when deactivated. That is deliberate — it is what stops a lost card being picked up and claimed by a stranger — but it does mean handing one on cannot be done from the dashboard. Get in touch with the code printed on the card and we will help. A promotional or giveaway card becomes claimable again once deactivated, and you can then tap it and activate it yourself. If it is your own card showing somebody else, do not try to fix it yourself — get in touch and tell us the code printed on the card.